The statement blamed the breakdown on a dispute over who would be eligible to vote in the south's January independence referendum, Voice of America reported Wednesday.
Negotiators for the two sides will meet again in Addis Ababa at the end of the month, the statement concluded.
At issue is whether Abyei would become part of the north or the south in the event the south votes to secede.
Immediately after the talks broke down, Sudan's vice president flew from Khartoum to the southern capital of Juba Tuesday for urgent talks with South Sudan's president.
The hastily arranged meeting followed the walkout of the southern delegation from the U.S.-mediated talks.
Diplomats told Voice of America the next round of talks will be stepped up a notch.